Colloquium: "Fourier Analysis on the Heisenberg Group"

Abstract: The Heisenberg group (3 x 3 uni-upper triangular matrices with elements in a ring) is a venerable mathematical object. Simple random walk on this group (pick one of the last two rows at random and add or subtract it to the row above, starting from the identity) leads to new corners of the subject. If the ring is finite (the integers mod n), we get to Harper's operator, Hofstaders' butterfly and the 10 Martini's problem. If the ring is Z or R Gower's 'higher Fourier analysis' comes in. I will try to explain all this to a general mathematical audience, trying to trick you into thinking about some of the many open problems.

Host: Rachel Roberts

Tea @ 3:45pm in room 200